I have my computer hooked up to my home audio system which is a Deenon 3808 and a pair of Axiom M3's.

I have a HT OMEGA Striker sound card in the computer. I'm using the SPDIF output from the sound card to the Denon. The sound card SNR is only 100db. Would my sound be better with a sound card that has a SNR of 124db?

No. A signal-to-noise ratio of "only" 100 dB is spectacularly good compared to the typical SNR found in analog gear-- about 60 dB for the best vinyl (most vinyl is much worse), a bit more for analog tape. There would be no audible advantage to moving from your current sound card to one with a greater than 100 dB S/N ratio.

Keep in mind that a noise floor that's -80 dB is totally inaudible with musical programming of any sort. Empirical tests that introduce distortion at increasing levels with the music have shown that the distortion is often not detected by trained listeners until the background distortion levels are increased to -40 dB to -30dB below the music signals.

Yes, in complete agreement with the points made by Alan and Chris. To put more numbers on it, the -30dB distortion mentioned by Alan is about 3% and -40dB is about 1%. Audibility varies with the type of music involved, but concerns sometimes seen in arguments elsewhere about distortion measurements differing by tenths or even hundredths of a percent aren't based on realities.